Table of Contents
- What Perpetuity Means in Finance
- Key Takeaways on Perpetuities
- Understanding Perpetuity
- The Finite Value of Infinite Cash Flows
- Perpetuity Present Value Formula
- Example of Perpetuity in Valuation
- Growing Perpetuities
- How Perpetuity Works in Investing
- Valuing a Perpetuity
- Difference Between Perpetuity and Annuity
- How Long Does a Perpetuity Last?
- The Bottom Line
What Perpetuity Means in Finance
Let me explain what a perpetuity is: it's a financial instrument that delivers continuous cash flows indefinitely, without any set end date. Think of it as an annuity that never stops. In today's world, actual perpetuities are pretty rare, but the idea sticks around in finance and economics. I define perpetuity as a steady stream of identical cash flows that goes on forever, and it's key in models like the dividend discount model (DDM).
Key Takeaways on Perpetuities
You should know that a perpetuity in finance is an investment paying out endless cash streams. To find its present value, divide the regular cash flows by the discount rate. There's also a growing perpetuity, where cash flows increase each period. While these products aren't common anymore, the perpetuity concept is still vital in finance.
Understanding Perpetuity
An annuity is basically a series of cash flows, like when a retiree invests in one for monthly income over years or a lifetime. A perpetuity is like that but eternal—the cash flows never end. In finance, we use perpetuity calculations to find the present value of a company's cash flows, discounted at a certain rate. Take British consols as a historical example: these bonds from the UK government paid annual interest forever, starting in 1751, and were a way to pass wealth across generations. The Bank of England ended them in 2015.
The Finite Value of Infinite Cash Flows
It might sound counterintuitive, but an infinite series of cash flows can have a finite present value. That's because of the time value of money—each future payment is worth less than the one before. In company valuations, we treat firms as going concerns that last forever, so the terminal year uses the perpetuity formula to capture that ongoing value.
Perpetuity Present Value Formula
Here's the formula for the present value of a perpetuity: PV = C / r, where PV is present value, C is the cash flow, and r is the discount rate. It's essentially summing up infinite discounted cash flows. For terminal values in valuations, it's more involved: take the year 10 cash flow, multiply by (1 + g), then divide by (r - g), where g is the growth rate.
Example of Perpetuity in Valuation
Suppose a company projects $100,000 in year 10, with an 8% cost of capital and 3% growth rate. The perpetuity value is ($100,000 × 1.03) / (0.08 - 0.03) = $2.06 million. That means $100,000 paid perpetually, growing at 3%, is worth $2.06 million in year 10 terms. Then, discount that back to today using present value methods.
Growing Perpetuities
A fixed perpetuity's value erodes over time due to inflation, making distant cash flows negligible. A growing perpetuity fixes this by increasing payments each period at a rate g, so the formula becomes PV = C / (r - g). This gives a higher present value than a fixed one, but remember, it assumes a constant growth rate, which isn't always realistic for businesses.
How Perpetuity Works in Investing
In investing, a perpetuity offers endless cash flows without maturity, unlike regular bonds. The UK's consols were a prime example until 2015—they paid interest indefinitely.
Valuing a Perpetuity
Even with infinite payments, a perpetuity has finite value because we discount future cash flows using DCF analysis, the same way we value stocks, bonds, or real estate.
Difference Between Perpetuity and Annuity
Both perpetuities and annuities provide fixed cash flows, but annuities end at a maturity date, while perpetuities go on forever. You can value both with DCF.
How Long Does a Perpetuity Last?
A perpetuity lasts forever, or at least until circumstances change drastically.
The Bottom Line
Perpetuities are investments with no end date, acting like infinite annuities. They're rare now, but the concept and its formula—cash flow divided by discount rate—are essential in finance for valuations.
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